Landau levels and magneto-optical properties of graphene ribbons

On the basis of Peierl coupling tight-binding model, we study the low energy magnetoelectronic properties of zigzag graphene ribbons by changing the ribbon width from the nanometer to the mesoscopic scale. The evolution of the Landau levels with the ribbon width shows that the number and the range of Landau levels are chiefly dominated by the ribbon width and the magnetic field (B). The Landau-level energies abide by the simple relation parallel to E parallel to proportional to root vertical bar n vertical bar B at low energy, not at the high energy (n subband index). However, a scaling law between the number of Landau levels and the ribbon width cannot be figured out. The Landau states occur only when the ribbon width is close to or greater than the distribution width of the Landau wave function and more Landau levels are generated with the increase in width. The low-frequency magnetoabsorption spectra reveal electronic properties and, thus, exhibit distinguishable delta-function-like peaks (Landau peaks). The peak height runs higher when the width increases, for more Landau states are allowed in a wider ribbon. The spectral frequencies of the Landau peaks are not determined by the ribbon width but by the field strength. The transition channels of the Landau peaks are identified and the selection rule is analyzed and discussed. The bearded defects can hardly affect the magnetoabsorption peaks due to the Landau levels. (c) 2008 American Institute of Physics.